Question: Simplify the following expression: $n = \dfrac{2r^2 - 12r - 14}{r - 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $2$ , so we can rewrite the expression: $ n =\dfrac{2(r^2 - 6r - 7)}{r - 7} $ Then we factor the remaining polynomial: $r^2 {-6}r {-7} $ ${-7} + {1} = {-6}$ ${-7} \times {1} = {-7}$ $ (r {-7}) (r + {1}) $ This gives us a factored expression: $\dfrac{2(r {-7}) (r + {1})}{r - 7}$ We can divide the numerator and denominator by $(r + 7)$ on condition that $r \neq 7$ Therefore $n = 2(r + 1); r \neq 7$